angle measure | rotation
0 0
π/6 1/12
π/4 1/8
π/2 1/4
2π/3 1/3
π 1/2
3π/2 3/4
2π 1
How to determine angle measure and rotation?An angle is a measure of the amount of turn between two lines or rays that share a common endpoint. The unit of measure for angles is usually degrees, but radians and gradians are also used.
Since 2π radian corresponds to 1 full rotation. We can say:
π/6 radian = π/6 * 1/2π = 1/12 rotation
1/8 rotation = 1/8 * 2π = π/4 radian
1/6 rotation = 1/6 * 2π = π/3 radian
π/2 radian = π/2 * 1/2π = 1/4 rotation
2π/3 radian = 2π/3 * 1/2π = 1/3 rotation
1/2 rotation = 1/2 * 2π = π radian
3π/2 radian = 3π/2 * 1/2π = 3/4 rotation
1 rotation = 2π radian
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Select the correct answer from each drop-down menu.
Line r cuts parallel lines p and q as shown in the figure.
Angles E and G are to each other because they are angles.
Answer:
see explanation
Step-by-step explanation:
angles E and G are congruent to each other because they are vertical angles.
The negation of the product of five times a number divided by two is ten?
The algebraic expression that can be represented by the statement is -5x/2 = 10
How to make a algebraic expression that can be represented by the statement?From the question, we have the following statement that can be used in our computation:
The negation of the product of five times a number divided by two is ten
Represent the variable with y
So, we have the following representation
The negation of the product of five times x divided by two is ten
Express the product as an actual product
So, we have the following representation
The negation of 5x divided by two is ten
Express the quotient as an actual quotient
So, we have the following representation
The negation of the 5x/2 is ten
Lastly, we have
-5x/2 = 10
Hence, the expression is -5x/2 = 10
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Carson owes Nigel $110. If Carson repays this debt at a rate of $15 per week, which graph best represents when, in weeks, Carson’s debt will be less than $50?
Responses
After doing the equitation the at rate of $15 per week.
How to do graph representation?
Graph representation is a way of visualizing data as a graph or chart. It is used to easily identify relationships between data points and to illustrate trends in the data. Graphs can be used to present data in a variety of ways, such as bar graphs, line graphs, pie charts, scatter plots and more. Graphs are especially useful when trying to compare two or more sets of data and to highlight any patterns or trends that may exist. Additionally, graphs are often used to represent numerical data in a more visually appealing way. By using graphs, it is easier to identify relationships, trends and outliers in the data. Graphs also help to make data easier to interpret and understand.
Carson owes = $110
At rate of $15 per week.
The graph representation will follows:
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Renata and ben each have 32 feet of wood for framing their rectangular murals. Renata makes her frame 18 ft high. Ben makes his frame 5 ft high. Whose mural has the greater area? How much greater?
Answer: Renata, \(416\ ft^2\)
Step-by-step explanation:
Given
The base of rectangular wood is \(b=32\ ft\)
The height of Renata frame is \(h_r=18\ ft\)
The height of the ben frame is \(h_b=5\ ft\)
The area of the rectangular frame is \(A=b\times h\)
The area of Renata frame is \(A_r=32\times 18=576\ ft^2\)
The area of the ben frame is \(A_b=32\times 5=160\ ft^2\)
Clearly, the area of Renata is more by \(576-160=416\ ft^2\)
Find the two values x can have if \(x^{2}\) - 14=50
The two values of x in the equation are x = -8 and x = 8
How to determine the values of x and y?The equation is given as
x² - 14 = 50
Add 14 to both sides of the equation
So, we have the following equation
x² - 14 + 14 = 50 + 14
Evaluate the like terms
So, we have the following equation
x² = 64
Take the square roots of both sides
√x² = ±√64
Evaluate the square roots
So, we have the following equation
x = ±8
Split
x = -8 and x = 8
Hence, the values are x = -8 and x = 8
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Write the inequality that represents the sentence.
The sum of a number and 5 is less than -7 .
The inequality that represents the sentence "The sum of a number and 5 is less than -7" is written as x + 5 < -7, where x represents the unknown number.
To represent the given sentence as an inequality, we need to translate the words into mathematical symbols. The phrase "The sum of a number and 5" can be written as x + 5, where x represents the unknown number. The phrase "is less than" indicates the use of the inequality symbol "<". Finally, the phrase "-7" represents the value that the sum is less than.
Combining these components, we can write the inequality x + 5 < -7. This inequality states that the sum of a number (represented by x) and 5 is less than -7.
Solving this inequality involves isolating the variable x on one side. By subtracting 5 from both sides of the inequality, we obtain x < -12 as the solution. This means that any value of x less than -12 will satisfy the original sentence, "The sum of a number and 5 is less than -7."
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The seventh grade enrollment at Main Middle School reduced from 615 students to 492 students. By What percentage was the number of students reduced?
Answer:
492 *100/625 =80 %
Step-by-step explanation:
Where [*]= Multiply
Please help me I’ll give you brainless it’s due in 20 minutes
I really need help po...
PERFORMANCE STANDARD:
Formulate and solve accurately situational problems involving derivatives using chain rule.
GOAL:
Your task is to come up with a model or situation involving chain rule based on gathered facts and data. You also need to accurately solve and cited situational problem and provide an explanation of your work.
ROLE:
You are an engineer, a mathematician, a physicist, a doctor, a business man or a real estate agent. Your job is to explain how derivatives can be utilized in order to predict future values.
AUDIENCE:
Your clients are Senior High students who are planning to be engineers, doctors, businessmen, and mathematicians.\
SITUATION:
You need to convince your audience that your model equation is correct based on gathered data and facts. It is empirical that the use of derivatives is given emphasis in order to predict the future values of model problem and situation.
PRODUCT:
You will prepare a short presentation of your output which includes:
picture, illustrations or drawing to aid in the visualization of your chosen problem or situation;
model equation of your problem;
comprehensive mathematical solution to the problem; and
objective generalization or conclusion of the problem.
STANDARDS:
You need to formulate and solve accurately situational problems involving chain rule.
Your product must meet the standards provided. (See attached rubrics.)
CATEGORY
-Diagrams and
Sketches
4
*Diagrams and/or
sketches are clear
and greatly add to
the reader/s’
understanding of
the procedure(s).
3
*Diagrams and/or
sketches are clear
and easy to
understand.
2
*Diagrams and/or
sketches are
somewhat difficult
to understand.
1
*Diagrams and/or
sketches are
difficult to
understand or are
not used.
-Mathematical
Concepts
4
*Explanation shows
complete
understanding of
the mathematical
concepts used to
solve the
problem(s).
3
*Explanation shows
substantial
understanding of
the mathematical
concepts used to
solve the
problem(s).
2
*Explanation shows
some
understanding of
the mathematical
concepts needed
to solve the
problem(s).
1
*Explanation shows
very limited
understanding of
the underlying
concepts needed
to solve the
problem(s) OR not
written.
-Mathematical
Technology and
Notation
4
*Correct
terminology and
notation are
always used,
making it easy to
understand what
was done.
3
*Correct
terminology and
notation are
usually used,
making it fairly
easy to
understand what
was done.
2
*Correct
terminology and
notation are used,
but it is sometimes
not easy to
understand what
was done.
1
*There is little use,
or a lot of
inappropriate use,
of terminology and
notation.
-Mathematical
Reasoning
4
*Uses complex and
refined
mathematical
reasoning.
3
*Uses effective
mathematical
reasoning.
2
*Some evidences
of mathematical
reasoning.
1
*Little evidence of
mathematical
reasoning.
-Mathematical
Errors
4
*90-100% of the
steps and
solutions have no
mathematical
errors.
3
*Almost all (85-
89%) of the steps
and solutions have
no mathematical
errors.
2
*Most (75-84%) of
the steps and
solutions have no
mathematical
errors.
1
*More than 75% of
the steps and
solutions have
mathematical
errors.
PS. The chosen role is a doctor.
An example of situational problems involving derivatives using chain rule is given below.
How to explain the problemA ladder is leaning against a wall. The base of the ladder is 6 feet from the wall and the top of the ladder is 8 feet above the ground. If the ladder is slipping down the wall at a rate of 2 feet per second, how fast is the base of the ladder moving away from the wall when the top of the ladder is 6 feet above the ground?
Let x be the distance from the base of the ladder to the ground, and let y be the distance from the top of the ladder to the ground. Then we have:
x² + y² = 10²
Differentiating both sides with respect to time t, we get:
2x(dx/dt) + 2y(dy/dt) = 0
We are given that dy/dt = -2 (because the ladder is slipping down the wall at a rate of 2 feet per second), and we want to find dx/dt when y = 6. To do this, we need to find x when y = 6:
x² + 6² = 10²
x² = 64
x = 8
Now we can substitute x = 8 and dy/dt = -2 into the equation we derived earlier and solve for dx/dt:
2(8)(dx/dt) + 2(6)(-2) = 0
16(dx/dt) - 24 = 0
dx/dt = 24/16 = 3/2
Therefore, the base of the ladder is moving away from the wall at a rate of 3/2 feet per second when the top of the ladder is 6 feet above the ground.
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can you please find x and explain it to me thanks
Answer:
28
Step-by-step explanation:
I'm not sure but like this
(ADC)=16
(ACB)=12
16+2=(DCB)=28
Erika paid a self-employment tax last year. She calculated the self-employment tax for different amounts of net earnings and recorded them in the table shown. Self-Employment Tax Net Earnings, x Self-Employment Tax, y $0 $0 $15,000 $2,295 $30,000 $4,590 $45,000 $6,885 Which function describes the relationship between x, the amount of net earnings, and y, the self-employment tax?
a y=15/2295x
b y=153/1000x
c y=1000/153x
d y=2295/15x
Answer:
B
Step-by-step explanation:
because i got a 100
i need help i don’t get this
Answer:
b = 2
c = -1
d = -2
Step-by-step explanation:
b = 2*1 = 2
c = -3 +b = -3+2 = -1
d = c*2 = -1 * 2 = -2
What is the answer to this integer equation??
5x - 1 - 3x = -1
Answer:
Step-by-step explanation:
5x - 3x -1 = -1
2x - 1 = -1
+1 +1
2x = 0
/2 /2
x = 0
please help meeeeeeee <33
Answer:
f(5) = 22; f(9) = 34
Step-by-step explanation:
f(5) = 3(5) +7
f(5) = 22
f(9) = 3(9) +7
f(9) = 34
in 2016 the better business bureau settled 80% of complaints they received in the united states. suppose you have been hired by the better business bureau to investigate the complaints they received this year involving new car dealers. you plan to select a sample of new car dealer complaints to estimate the proportion of complaints the better business bureau is able to settle. assume the population proportion of complaints settled for new car dealers is 0.80, the same as the overall proportion of complaints settled in 2016. (a) suppose you select a sample of 220 complaints involving new car dealers. show the sampling distribution of p.
The sampling distribution of p is approximately normal with a mean of 0.80 and a standard error of 0.00309.
The sampling distribution of p can be determined using the formula for standard error.
Step 1: Calculate the standard deviation (σ) using the population proportion (p) and the sample size (n).
σ = √(p * (1-p) / n)
= √(0.80 * (1-0.80) / 220)
= √(0.16 / 220)
≈ 0.0457
Step 2: Calculate the standard error (SE) by dividing the standard deviation by the square root of the sample size.
SE = σ / √n
= 0.0457 / √220
≈ 0.00309
Step 3: The sampling distribution of p is approximately normal, centered around the population proportion (0.80) with a standard error of 0.00309.
The sampling distribution of p is a theoretical distribution that represents the possible values of the sample proportion. In this case, we are interested in estimating the proportion of complaints settled for new car dealers. The population proportion of settled complaints is assumed to be the same as the overall proportion of settled complaints in 2016, which is 0.80.
To construct the sampling distribution, we calculate the standard deviation (σ) using the population proportion and the sample size. Then, we divide the standard deviation by the square root of the sample size to obtain the standard error (SE).
The sampling distribution is approximately normal, centered around the population proportion of 0.80. The standard error reflects the variability of the sample proportions that we would expect to see in repeated sampling.
The sampling distribution of p for the selected sample of new car dealer complaints has a mean of 0.80 and a standard error of 0.00309. This information can be used to estimate the proportion of complaints the Better Business Bureau is able to settle for new car dealers.
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[3 pts] you and one of your study group members toss a fair coin n times. show that the probability that both of you toss the same number of heads is (2n n )2−2n
the probability that both you and your study group member toss the same number of heads when flipping a fair coin n times is (2n choose n)^2 / 2^n.
To show that the probability of both you and your study group member tossing the same number of heads when flipping a fair coin n times is (2n choose n)^2 / 2^n, we can use the concept of binomial coefficients.
Let's assume that you and your study group member each flip the coin n times. The total number of possible outcomes for each person is 2^n since there are two possible outcomes (heads or tails) for each flip.
Now, let's consider the number of ways in which you and your study group member can both have the same number of heads. Suppose the number of heads you both have is k, where k can range from 0 to n.
The number of ways you can have k heads in n flips is given by (n choose k), and the number of ways your study group member can also have k heads is also (n choose k) since the coin flips are independent.
Since you and your study group member can independently have any value of k heads ranging from 0 to n, the total number of outcomes where you both have the same number of heads is the sum of (n choose k) * (n choose k) for k = 0 to n. This can be represented as:
Σ[(n choose k) * (n choose k)] for k = 0 to n
Using the identity (n choose k) * (n choose k) = (2n choose n), we can rewrite the sum as:
Σ[(2n choose n)] for k = 0 to n
Since the binomial coefficient (2n choose n) is the same for all terms of the sum, we can simplify the sum by multiplying (2n choose n) by the number of terms (n + 1):
(n + 1) * (2n choose n)
Finally, we divide this by the total number of possible outcomes (2^n * 2^n) to get the probability:
[(n + 1) * (2n choose n)] / (2^n * 2^n)
Using the property (2n choose n) = (2n)! / (n! * n!), we can simplify further:
[(n + 1) * (2n)! / (n! * n!)] / (2^n * 2^n)
Simplifying the expression, we get:
[(n + 1) * (2n)!] / (n! * n! * 2^n * 2^n)
Now, notice that (2n)! = (2n * (2n - 1) * ... * 2 * 1) and that n! * n! = n!^2. Since there are n factors in both the numerator and denominator, we can rewrite (2n)! / (n! * n!) as (2n choose n).
Finally, substituting this back into the expression, we have:
[(n + 1) * (2n choose n)] / (2^n * 2^n)
Which is equal to (2n choose n)^2 / 2^n, as desired.
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Clue 1
The number has three digits.
Clue 2 The number is less than 140.
Clue 3 The number has 7 as a factor.
Clue 4 The number is even.
Clue 5 The sum of the digits of the number is less than 9.
Find the value of S
1/3 s + 14 = 26
Step-by-step explanation:
1/3 s + 14 = 26
1/3 s = 26 - 14
1/3 s = 12
s = 3 * 12
s = 36 (ANS)
Answer:
S=36
Step-by-step explanation:
You first turn the 14 into 0 by -14. Then you do it on the other side of the equall sign. Then you times 3 with the 1 on top and then times 12 by three. and botta boom botta bang theres your answer
5 people all of different age are sitting around a round table, what is the probability they are sitting in age order.
The probability that they are sitting around a round table in age order is 1/12. There are 10 ways for five people to sit in age order.
What is probability?Probability is a numerical description of how possible an event to happen. Probability of an event can be expressed as
P(A) = n(A) / n(S)
Where
P(A) is the probability of an event An(A) is the number of favorable outcomesn(S) is the total number of events in the sample spaceFive people all of different age are sitting around a round table.
Find the probability they are sitting in age order!
Let's name the 5 people 1, 2, 3, 4, 5.
There are two ways in putting them in the age order, ascending or descending.
Ascending: 12345, 23451, 34512, 45123, 51234.Descending: 54321, 43215, 32154, 21543, 15432.There are 10 ways that they are sitting around a round table in the age order.
n(Age order) = 10
The total arrangements for 5 people sitting around a round table is
5! = 1 × 2 × 3 × 4 × 5
5! = 120 ways
n(S) = 120
The probability that they are sitting in age order would be
P(Age order) = n(Age order) / n(S)
P(Age order) = 10/120
P(Age order) = 1/12
Hence, the probability that five people are sitting around a round table in age order is 1/12.
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The shape is composed of three squares and two semicircles. Select all the expressions that correctly calculate the perimeter of the shape.
The expression that correctly calculates the perimeter of the shape is given as follows:
P = 2(6s + πr).
In which:
s is the side length of the square.r is the radius of the semicircle.How to obtain the perimeter of the square?The perimeter of a square of side length s is given as follows:
P = 4s.
Hence, for three squares, the perimeter is given as follows:
P = 3 x 4s
P = 12s.
How to obtain the perimeter of a semi-circle?The perimeter, which is the circumference of a semicircle of radius r, is given by the equation presented as follows:
C = πr.
Hence the perimeter of two semicircles is given as follows:
C = 2πr.
How to obtain the perimeter of the shape?The perimeter of the entire shape is given by the sum of the perimeter of each shape, hence:
P = 12s + 2πr.
P = 2(6s + πr).
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Which are vertical angles?
Answer:
The top answer is correct
Step-by-step explanation:
Vertical angles are formed when two lines meet each other at a point and they are always equal to each other. Their angles are also equal. In this problem number two has angles that do not match and number three also has different angles. Finally number four also has different angles and is not equal to each other. Leaving number one (the top answer) which looks to have the same angle, and is equal to each other.
Test for symmetry and then graph the polar equation 4 sin 8.2 cose a. Is the graph of the polar equation symmetric with respect to the polar axis ? OA The polar equation failed the test for symmetry which means that the graph may or may not be symmetric with respect to the polar as OB. The polar equation failed the test for symmetry which means that the graph is not symmetric with respect to the poor as OC. Yes
The polar equation 4 sin 8.2 cose a failed the test for symmetry. The graph may or may not be symmetric with respect to the polar axis.
The polar equation is given by 4 sin(8.2 * theta). To test for symmetry, we can substitute negative theta values into the equation and check if the resulting points are symmetric to the points obtained by substituting positive theta values.
If the equation fails the symmetry test, it means that the resulting points for negative theta values are not symmetric to the points obtained for positive theta values. In this case, since the equation failed the symmetry test, the graph may or may not be symmetric with respect to the polar axis. We cannot conclude definitively whether it is symmetric or not based on the information given.
To determine the symmetry of the graph, it would be helpful to plot the polar equation and visually analyze its shape. However, the information provided does not include the complete polar equation or a graph, so we cannot determine the exact symmetry of the graph from the given information.
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If 140 men working 10 hours a day can build a house in 16 days, find out how many men will build same kind of house in 12 days by working 13 hours a day?
We need 144 men to build the house in 12 days working 13 hours a day.
Let M be the number of men needed to build the house in 12 days working 13 hours a day.
140 x 10 x 16 = M x 13 x 12
Simplifying the equation, we get:
22400 = 156M
Dividing both sides by 156, we get:
M = 144.1
An equation in mathematics is a statement that two expressions are equal. It consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). The expressions on either side can be numbers, variables, or combinations of both. The equation expresses that the values of the expressions on both sides are equivalent.
Equations play a fundamental role in many areas of mathematics and are used to model various real-world situations, such as physics, engineering, and finance. They can be solved using various techniques, such as substitution, elimination, or graphing, to find the values of the variables that satisfy the equation.
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Lee Jenkins worked the following hours as a manager for a local Pizza Hut 5 4/1,9 4/3,7 4/3 and 8 4/3. How many total hours did Lee work?
Lee Jenkins worked the following hours as a manager for a local Pizza Hut 5 4/1, 9 4/3, 7 4/3 and 8 4/3.
Now, the above-mentioned hours are not in the proper form that we are required to calculate. Therefore, we need to change them into the proper format .In order to add these hours, we must first convert the hours and minutes to the same format.
We'll need to convert each fraction to a common denominator of 3x3=9. 5 4/1 in the mixed format is 5 + 4/1,
which is equal to 9. 9 4/3 in the mixed format is 9 + 4/3,
which is equal to 10 1/3.7 4/3 in the mixed format is 7 + 4/3,
which is equal to 8 1/3.8 4/3 in the mixed format is 8 + 4/3,
which is equal to 9 1/3.Now that we've converted the times,
we can add them together to get a total of 36 1/3 hours.
Therefore, Lee worked for 36 1/3 hours. the total number of hours Lee worked as a manager for the local Pizza Hut is 36 1/3 hours.
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the most commonly shaped base in pin curls is the _____ base. A. Arc base. B. Rectangular base. C. Panel base.
The most commonly shaped base in pin curls is the rectangular base.
This is the main answer to your question. An explanation for this is that the rectangular base is versatile and can be used for creating various sizes of curls. Additionally, it allows for easy control of the curl direction. In conclusion, when creating pin curls, the rectangular base is the most commonly used due to its versatility and ease of use.
The arc base, also known as the half-moon or C-shape base, is the most popular base shape for pin curls because it allows for better distribution of the hair and provides more natural-looking curls. This shape helps prevent splits in the finished hairstyle, ensuring a smoother and more cohesive appearance.
In pin curls, the arc base is the most commonly used base shape due to its ability to create natural-looking curls and prevent splits in the hairstyle.
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Rosa is driving from Los Angeles to San Francisco. Because of some heavy traffic, she covers a distance of 5 miles in 30 minutes. How many miles does Rosa travel in 48 minutes? PLS HELPPPP:)
Answer:
8 miles.
Step-by-step explanation:
Answer:
8 miles
Step-by-step explanation:do 30divided by 6 which eqauls 5 which is shown above then do the same for 48 which eqauls 8 plzz mark as brainliest
Stock Repurchase [LO4] Awake Corporation is evaluating an extra dividend ver- sus a share repurchase. In either case, $17,500 would be spent. Current earnings are $1.89 per share, and the stock currently sells for $64 per share. There are 2.000 shares outstanding. Ignore taxes and other imperfections in answering the first two questions. Evaluate the two alternatives in terms of the effect on the price per share of the stock and shareholder wealth. What will be the effect on the company's EPS and PE ratio under the two different scenarios
The effect under the scenarios are:
Choosing the extra dividend option would result in a decrease in the stock price per share and a decrease in the PE ratio.Choosing the share repurchase option would result in a lower stock price per share,The extra dividendTotal Dividend = $17,500
Dividend per Share = Total Dividend / Number of Shares
= $17,500 / 2,000
= $8.75 per share
Effect on Share Price:
Typically, when a dividend is paid, the stock price tends to decrease by the amount of the dividend. Therefore, the stock price per share would decrease by the dividend per share:
New Stock Price per Share = Current Stock Price - Dividend per Share
= $64 - $8.75
= $55.25
New Shares Outstanding = Current Shares Outstanding - Number of Shares Repurchased
= 2,000 - 273.44
= 1,726.56 shares
New Stock Price per Share = Total Amount Spent / New Shares Outstanding
= $17,500 / 1,726.56
= $10.14
EPS = Earnings / Number of Shares
= $1.89 / 2,000
= $0.000945
The PE (Price-to-Earnings) ratio is calculated by dividing the stock price per share by the EPS. Let's calculate the PE ratio under each scenario:
PE Ratio before the decision = Stock Price / EPS
= $64 / $0.000945
= 67772.49
PE Ratio with Extra Dividend = New Stock Price per Share / EPS
= $55.25 / $0.000945
≈ 58413.92
PE Ratio with Share Repurchase = New Stock Price per Share / EPS
= $10.14 / $0.000945 ≈ 10727.51
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What are the ways to prove triangle congruence A for any triangle B for right triangles?.
The ways to prove right triangles congruence:
Triangle in the right position
Congruent Hypotenuse-Angle.
Leg-Angle Consistency
Hypotenuse–Leg Congruence
What is a right-angle triangle?
It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
According to the RHS Criterion:
If the hypotenuse and one of the sides of a right-angled triangle match the hypotenuse and the corresponding side of another right-angled triangle, then the two triangles are said to be congruent.
Leg-to-leg coherence Right triangles are said to be congruent if their respective legs match up with those of another right triangle.
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jack paid $99 for 6 pizzas. How much did he pay per pizza?
Answer:
99/6=16.5 per pizza
have u good day
Answer:
16 and a half, ($16.50)
Step-by-step explanation:
99 / 6 = 16.5
On a test called the MMPI-2, a score of 30 on the Anxiety Subscale is considered
very low. Felipe participates in a yoga group at his gym and decides to give this
subscale to 18 people in his yoga group. The mean of their scores is 35.2, with a standard deviation of 10.4. He wants to determine whether their anxiety scores are statistically equal to 30.
What are the groups for this one-sample t-test?
What is the null hypothesis for this one-sample t-test?
What is the value of "?
Should the researcher conduct a one- or two-tailed test?
What is the alternative hypothesis?
What is the value for degrees of freedom?
What is the t-observed value?
What is(are) the t-critical value(s)?
Based on the critical and observed values, should Felipe reject or retain the null
hypothesis? Does this mean that his yoga group has scores that are above 30, below 30, or
statistically equal to 30?
What is the p-value for this example?
What is the Cohen’s d value for this example?
If the " value were dropped to .01, would Felipe reject or retain the null hypothesis?
Calculate a 42% CI around the sample mean.
Calculate a 79% CI around the sample mean.
Calculate a 95% CI around the sample mean.
The MMPI-2 test is used for the assessment of psychopathology and personality of patients.
It includes 567 true-false questions, resulting in 10 clinical scales, among which one is the anxiety subscale.
A score of 30 or less is usually considered very low.
The questions are answered by the patient, usually in a clinical or research setting.
A one-sample t-test is conducted in the problem, whereby a sample of 18 participants in a yoga group is tested for anxiety scores.
The following are the parameters of the one-sample t-test:Groups:
18 participants
Null hypothesis: The anxiety scores of Felipe's yoga group are statistically equal to 30." value: 30
Type of test: One-tailed test
Alternative hypothesis: The anxiety scores of Felipe's yoga group are greater than 30.
Degrees of freedom: n - 1 = 17T-observed value: (35.2 - 30) / (10.4 / sqrt(18)) = 2.41T-critical value: 1.734
Reject or retain null hypothesis: Since the t-observed value (2.41) is greater than the t-critical value (1.734), Felipe should reject the null hypothesis, which implies that his yoga group's scores are greater than 30.P-value: 0.014Cohen’s d value: (35.2 - 30) / 10.4 = 0.5
If the " value were reduced to 0.01, Felipe would still reject the null hypothesis, since the p-value (0.014) is lower than the alpha level (0.01).
For the sample mean: 35.2CI for 42%: 35.2 ± 0.58CI for 79%: 35.2 ± 1.16CI for 95%: 35.2 ± 2.13
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